REFINEMENTS AND REVERSES OF FEJER’S ´ INEQUALITIES FOR CONVEX FUNCTIONS ON LINEAR SPACES

Abstract

In this paper, we establish some refinements and reverses of the celebrated F´ejer’s inequalities for the general case of functions defined on linear spaces. The obtained bounds are in terms of the Gˆateaux lateral derivatives. Some applications for norms and semi-inner products in normed linear spaces are also provided.

Keywords

• convex functions
• integral inequalities
• hermite-hadamard inequality
• f´ejer’s inequalities